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If (a+b)/(b+c) = (c+d)/(d+a) then prove ...

If `(a+b)/(b+c) = (c+d)/(d+a)` then prove that either c= a or a+b+c+d = 0.

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UNITED BOOK HOUSE-SUGGESSTION OR MADHYAMIK PARIKSHA-EXERCISE
  1. If (a^3+3ab^2)/(3a^2b+b^3) = 63/62 the find (5a-3b):(3a-b).

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  2. If a,b,c,d are in continued proportion then show that bc(1/a+1/b+1/c+1...

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  3. If (a+b)/(b+c) = (c+d)/(d+a) then prove that either c= a or a+b+c+d = ...

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  4. If ay - bx/c = cx - az/b = bz - cy/a, then prove that x/a = y/b = z/c.

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  5. Prove that the front angle formed at the centre of a circle by an arc ...

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  6. Prove that opposite angles of a cyclic quadrilateral are supplementary

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  7. State and prove Pythagoras theorem.

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  8. If two circles touch each other externally then the point of contact w...

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  9. State and prove the convere of the Pythagoras theorem.

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  10. Prove that two equal chords are equidistant from the centre of the cir...

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  11. If two chords AB and CD of a circle with centre O, when produce inters...

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  12. ABCD is a cyclic quadrilateral. The bisectors of angleDAB and angleBCD...

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  13. In a isosceles triangle ABC , angleB is right angle. Bisector of angle...

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  14. Draw a triangle ABC, whose AB = 4.5 cm , BC = 3.5cm and angleABC = 90^...

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  15. Draw an equilateral triangle having each side of length 6.5 cm. Now dr...

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  16. Draw a triangle ABC whose BC = 9 cm, AB = 7 cm and AC = 8cm. Now draw ...

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  17. Draw a triangle having sides 6cm, 8 cm and 10 cm. Now draw the incircl...

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  18. If cos theta - sin theta = sqrt2 sin theta, then show that cos theta+s...

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  19. If the difference between two acute angles of a right angled triangle ...

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  20. Solve: (x+1) cot^2 (pi/6) = 2cos^2 (pi/3)+ 3/4 sec^2 (pi/4)+ 4 sin^2 (...

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